368 
PROFESSOR M. J. M. HILL OH THE MOTION OF FLUID, PART 
du 
dt 
dv 
dt 
du , du d f [dp TT 
+“*+^=-4 ) 7 +a 
+-£+*S--f»(ff+ T 
' , p +^ W +^( p ")= 0 
From which can be deduced 
d d d 
dt+ U dx^ V dy/ 
dv du 
dx dy 
= 0 
Now regarding this as a particular case of motion in three dimensions in which 
iv=0, the motion being parallel to the plane 2 = 0 , it is possible to put by means of 
Clebsch’s forms 
Therefore 
•=£+AHt+‘? 
d , d 
dt +U dx +V dy, 
. | dX dp dX dp 
dx dy dy dx r — 0 
This result has been deduced from the three equations of motion, and Clebsch’s 
forms for the components of the velocity. 
But it can be deduced from the equation of continuity alone and the following 
equations known to be satisfied by X, p. 
Therefore 
dX , dX , dX 
— -\-u -7- -\-v —- =0 
dt dx dy 
dp . dp c ^ 2 t__ n 
7, -\~u , -\-v —0 
dt dx dy 
dX 
dX 
dX 
dX 
dt 
dy 
dx 
dt 
dp 
dip- 
dp 
dp 
dt 
dy 
n 
dx 
dt 
dX 
dX 
and v — 
dX 
dX 
dx 
dy 
dx 
dy 
dp 
dp 
dp 
dp 
dx 
dy 
dx 
dy 
